On the Measurement of Magnifying Powers of Optical Instruments

The magnifying power of any optical instrument is the ratio of the angle subtended at the eye by the image as seen in the instrument to the angle subtended at the eye by the object when seen directly. If the object to be seen is at a short distance from the eye, and the distance can be altered, the eye must always be placed so that the object is at the distance of most distinct vision (on the average, 25 cm.); and any optical instrument is focussed so that the image seen is at the distance of most distinct vision. Thus the magnifying power of a lens or microscope is the ratio of the angle subtended at the eye by the image in the instrument to the angle subtended at the eye by the object when placed at the distance of most distinct vision.

Telescopes are, however, generally used to observe objects so distant that any alteration which can be made in the distance by moving the eye is very small compared with the whole distance, and hence for a telescope the magnifying power is the ratio of the angle subtended by the image in the telescope to the angle subtended by the object Then again this image is at the distance of distinct vision for the eye, but the focal length of the eye-piece is generally so short that the angle subtended by the image at the eye is practically the same as if the eye-piece were focussed so that the image was at an infinite distance.

Thus suppose the small image pq (fig. 29), formed by the object-glass A, is in such a position with reference to the eye-piece B that the image of it P'Q' formed by the eyepiece is at the same distance as the object PQ.

Since the object is very distant the angle subtended by it at the centre a of the object-glass, which is equal to the angle paq, is practically the same as that subtended by it at the eye, and the angle subtended by the image at the eye is practically the same as the angle pbq.

These angles being very small, they will be proportional to their tangents, and the magnifying power will be equal to either (1) the ratio of the focal length of the object-glass to the focal length of the eye-piece; or (2) the ratio of the absolute magnitude (diameter) of the image P'Q' to that of the object PQ when the telescope is so focussed that these two are at the same distance from the eye.

On this second definition of the magnifying power depends the first method, described below, of finding the magnifying power of a telescope.